The following table gives the scores of 30 students in a mathematics examination. scores 90–99 80–89 70–79 60–69 50–59 students 3 7 12 4 4 find the mean and the standard deviation of the given data. hint: assume that all scores lying within a group interval take the middle value of that group. (round your answers to two decimal places.)

Problems and applications q5 four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. here is their willingness to pay for each film: willingness to pay (dollars) shen antonio dmitri jake first film 10 9 8 3 second film 8 7 6 2 third film 6 5 4 1 fourth film 4 3 2 0 fifth film 2 1 0 0 within the dorm room, the showing of a movie a public good. if it costs $12 to rent a movie, the roommates should rent movies in order to maximize the total surplus. suppose the roommates choose to rent the optimal number of movies you just indicated and then split the cost of renting equally. this means that each roommate will pay $ .